Use our free GCF of Fractions Calculator tool to compute the GCF of 122/75, 298/765 i.e 2/3825 easily. The following is the detailed procedure to determine the greatest common factor of fractions 122/75, 298/765.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 122/75,298/765
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 122/75,298/765, numerators are 122,298
Denominators are 75,765
The GCF of 122,298 is 2 .
LCM of 75,765 is 3825.
The greatest common factor of 122/75,298/765 = [GCF of 122,298]/[LCM of 75,765]= 2/3825
Therefore, the GCF of 122/75,298/765 is 2/3825.
To find the highest common factor of 122,298, we have to find the factors of both numbers and list the highest common factor.
The factors of 122 are 1, 2, 61, 122
The factors of 298 are 1, 2, 149, 298
The HCF of 122,298 is 2.
Lets's calculate GCF of 122,298
2 | 122, 298 |
61, 149 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 122
:1,2,61,122
Now, list down the factors of 298
:1,2,149,298
Greatest Common Factor
We found the factors 122,298 . The biggest common factor number is the GCF number.
So the greatest common factor 122,298 is 2.
Lets's calculate LCM of 75,765
3 | 75, 765 |
5 | 25, 255 |
5, 51 |
∴ So the LCM of the given numbers is 3 x 5 x 5 x 51 = 3825
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/3825
Therefore, the GCF of Fractions 122/75,298/765 is 2/3825
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 75,765 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,765) = 15
common factors(in case of two or more numbers have common factors) = 1
GCF(75,765) x common factors =15 x 1 = 15
LCM(75,765) = ( 75 × 765 ) / 15
LCM(75,765) = 57375 / 15
LCM(75,765) = 3825
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 122,298?
The HCF of 122,298 is 2
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 122/75, 298/765?
Answer: GCF of Numerators as per given numbers 122/75, 298/765 is
GCF of Numerators i.e. for 122,298 is 2
LCM of denominators i.e. for 75,765 is 3825.
Thus, GCF of Fractions is 2/3825.Finally, GCF of Fractions for 122/75, 298/765 is 2/3825.